# GDP/Capita Confound Probe: Demographics → Interest Rates

Does GDP/capita absorb the demographic signal on rates?


## Key Results

| Dep Var | Sample | Model | Z₁ coef | Z₁ p | log_gdp_pc coef | log_gdp_pc p | Z₁×log_gdp_pc coef | Z₁×log_gdp_pc p | N | R² |
|:---|:---|:---|---:|---:|---:|---:|---:|---:|---:|---:|
| lending_rate | Full | M1: Z baseline | -31.35 | 0.1031 |  |  |  |  | 2572 | 0.128 |
| lending_rate | Full | M2: Z + GDP/pc | -38.64** | 0.0498 | -0.19 | 0.8824 |  |  | 2453 | 0.139 |
| lending_rate | Full | M3: Horse race | -36.03* | 0.0609 | -5.59*** | 0.0001 | -3.48*** | 0.0000 | 2453 | 0.193 |
| lending_rate | OECD | M1: Z baseline | 28.67 | 0.6096 |  |  |  |  | 440 | 0.542 |
| lending_rate | OECD | M2: Z + GDP/pc | -47.81 | 0.3468 | -20.61*** | 0.0000 |  |  | 416 | 0.632 |
| lending_rate | OECD | M3: Horse race | -84.25 | 0.1018 | -17.50*** | 0.0000 | 4.92*** | 0.0052 | 416 | 0.641 |
| lending_rate | Non-OECD | M1: Z baseline | -39.91* | 0.0567 |  |  |  |  | 2132 | 0.101 |
| lending_rate | Non-OECD | M2: Z + GDP/pc | -46.87** | 0.0295 | 2.16 | 0.1178 |  |  | 2037 | 0.119 |
| lending_rate | Non-OECD | M3: Horse race | -42.37** | 0.0470 | -4.41** | 0.0155 | -3.37*** | 0.0000 | 2037 | 0.145 |

## Attenuation Summary

| Dep Var | Sample | Z₁ baseline | Z₁ + GDP/pc | Attenuation % |
|:---|:---|---:|---:|---:|
| lending_rate | Full | -31.35 | -38.64** | -23.2% |
| lending_rate | OECD | 28.67 | -47.81 | 266.8% |
| lending_rate | Non-OECD | -39.91* | -46.87** | -17.4% |

*Attenuation >50% suggests GDP/capita substantially confounds demographics.*
*Significant Z₁×log_gdp_pc interaction means demographics operate differently across income levels.*

## Bond Yield Results (OECD-only, 23 countries)

| Dep Var | Model | Z₁ coef | Z₁ p | log_gdp_pc | log_gdp_pc p | Z₁×log_gdp_pc | interaction p | N | R² |
|:---|:---|---:|---:|---:|---:|---:|---:|---:|---:|
| govt_bond_10y | M1: Z baseline | 58.54*** | 0.004 | — | — | — | — | 711 | 0.291 |
| govt_bond_10y | M2: Z + GDP/pc | 25.77 | 0.168 | -10.28*** | <0.001 | — | — | 635 | 0.425 |
| govt_bond_10y | M3: Horse race | 47.40** | 0.024 | -9.69*** | <0.001 | -2.49** | 0.030 | 635 | 0.440 |
| short_rate_3m | M1: Z baseline | 65.92*** | 0.008 | — | — | — | — | 721 | 0.338 |
| short_rate_3m | M2: Z + GDP/pc | 21.28 | 0.353 | -10.34*** | <0.001 | — | — | 636 | 0.435 |
| short_rate_3m | M3: Horse race | 16.11 | 0.534 | -10.43*** | <0.001 | 0.62 | 0.646 | 636 | 0.431 |

### Bond Yield Attenuation

| Dep Var | Z₁ baseline | Z₁ + GDP/pc | Attenuation % | Horse race Z₁ | Recovers? |
|:---|---:|---:|---:|---:|:---|
| govt_bond_10y | 58.54*** | 25.77 | 56.0% | 47.40** | YES — interaction significant |
| short_rate_3m | 65.92*** | 21.28 | 67.7% | 16.11 | NO — fully absorbed |

### Interpretation

**10y bond yields**: GDP/capita confounds ~56% of the demographic signal, but the horse race with interaction *recovers* Z₁ significance (47.4**, p=0.024). The negative interaction (-2.49**, p=0.03) means demographics depress yields more strongly in lower-income OECD members (Greece, Turkey, Mexico, Chile). Demographics retain independent explanatory power for long-term rates.

**3m short rates**: GDP/capita absorbs ~68% and the horse race does not recover Z₁. Demographics do not independently predict short rates once income is controlled. The short rate finding in the asset returns paper (Z₁=60.1***) is likely capturing income effects.

**Lending rates (140-country)**: GDP/capita does NOT absorb Z₁ — actually strengthens it (-23% negative attenuation). The confound is OECD-specific, operating through the high correlation between aging and economic development within advanced economies.

**Implications for other papers**: The asset returns murder-suicide finding on 10y yields (Z₁≈44**) survives this test — the horse race Z₁=47.4** is essentially the same magnitude. The 3m rate finding is weaker. The Carvalho channel decomposition in gravity bilateral (23% rate-mediated) may be slightly overstated but is not fundamentally undermined.